Details of a fast and sustainable bottom-up process to grow large area high quality graphene films without the aid of any catalyst are reported in this paper. We used Melaleuca alternifolia, a volatile natural extract from tea tree plant as the precursor. The as-fabricated graphene films yielded a stable contact angle of 135°, indicating their potential application in very high hydrophobic coatings. The electronic devices formed by sandwiching pentacene between graphene and aluminum films demonstrated memristive behavior, and hence, these graphene films could find use in nonvolatile memory devices also.